A suspension system is being designed for a \(1000 \mathrm{~kg}\) vehicle. A first model of the system used in the design process is a spring of stiffness \(k\) in parallel with a viscous damper of damping coefficient \(c\). The model is being analyzed as the vehicle traverses a road with a sinusoidal contour, \(y(z)=Y \sin (2 \pi z / d)\) when the vehicle has a constant horizontal speed \(v\). The suspension system is to be designed such that the maximum acceleration of the passengers is \(2.5 \mathrm{~m} / \mathrm{s}^{2}\) for all vehicle speeds less than \(60 \mathrm{~m} / \mathrm{s}\) for all reasonable road contours. It is estimated that for such contours, \(Y<0.01 \mathrm{~m}\) and \(0.2 \mathrm{~m}